B1 - definition of a cyclic group

cyclic group

a group $G$ is cyclic if $a \in G$ such that $G = {a^{n} | n \in Z}$ , and $a$ is said to be its generator

G = ⟨ a ⟩

Z_{8} = ⟨ 1 ⟩ = ⟨ 3 ⟩ = ⟨ 5 ⟩ = ⟨ 7 ⟩